Gas turbine engines are used to power aircraft, watercraft, power generators, pumps, and the like. Gas turbine engines operate by compressing atmospheric air, burning fuel with the compressed air, and then removing work from hot high-pressure air produced by combustion of the fuel in the air. Rows of rotating blades and non-rotating vanes are used to compress the air and then to remove work from the high-pressure air produced by combustion. Each blade and vane has an airfoil that interacts with the gasses as they pass through the engine.
Airfoils have natural vibration modes of increasing frequency and complexity of the mode shape. The simplest and lowest frequency modes are typically referred to as the first bending mode, the second bending mode, the third bending mode, and the first torsion mode. The first bending mode is a motion normal to the working surface of an airfoil in which the entire span of the airfoil moves in the same direction. The second bending mode is similar to the first bending mode, but with a change in the sense of the motion somewhere along the span of the airfoil, so that the upper and lower portions of the airfoil move in opposite directions. The third bending mode is similar to the second bending mode, but with two changes in the sense of the motion somewhere along the span of the airfoil. The first torsion mode is a twisting motion around an elastic axis, which is parallel to the span of the airfoil, in which the entire span of the airfoil, on each side of the elastic axis, moves in the same direction.
Blades are subject to destructive vibrations induced by unsteady interaction of the airfoils of those blades with gasses passing through a gas turbine engine. One type of vibration is known as flutter, which is an aero-elastic instability resulting from the interaction of the flow over the airfoils of the blades and the blades' natural vibration tendencies. The lowest frequency vibration modes, the first bending mode and the first torsion mode, are often the vibration modes that are susceptible to flutter. When flutter occurs, the unsteady aerodynamic forces on the blade, due to its vibration, add energy to the vibration, causing the vibration amplitude to increase. The vibration amplitude can become large enough to cause damage to a blade. Another type of vibration is known as forced response, which is an aero-elastic response to inlet distortion or wakes from upstream airfoils, struts, or any other flow obstruction. The operable range, in terms of pressure rise and flow rate, of turbomachinery can sometimes be restricted by flutter or forced response phenomena.
The specific susceptibility of a blade to flutter may be increased if all the blades on a rotor are identical in terms of their vibration frequencies. Sometimes, intentional variations may be introduced into blades during manufacturing to create structural mistuning of a rotor and provide flutter resistance.
The specific susceptibility of a blade to forced response may be increased if random manufacturing variations would put a blade at or near the peak amplification factor based on mistuning. Sometimes, intentional variations may be introduced into blades during manufacturing to create structural mistuning of a rotor to reduce the amplification factor due to random mistuning.